Pengendalian Polusi Udara Terhadap Penyakit Pernapasan

Nuriska, Salwa (2025) Pengendalian Polusi Udara Terhadap Penyakit Pernapasan. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Peningkatan polusi udara akibat aktivitas industrialisasi maupun urbanisasi menjadi masalah serius bagi kesehatan masyarakat, terutama dalam memicu penyakit pernapasan. Polutan udara yang terdiri dari partikel tertentu dan zat-zat berbahaya memiliki dampak langsung terhadap fungsi pernapasan. Dalam Tugas Akhir ini dibahas mengenai model polusi udara yang mempengaruhi penyebaran penyakit pernapasan, yang terdiri dari tiga variabel, yaitu populasi rentan (S(t)), populasi terinfeksi (I(t)), dan konsentrasi polutan udara (F(t)), di mana (S(t)) merupakan variabel tambahan setelah dilakukan modifikasi model. Model penyebaran penyakit pernapasan direpresentasikan melalui model SIS untuk menggambarkan penyebaran penyakit pernapasan pada populasi manusia. Selanjutnya, untuk mengurangi individu terinfeksi penyakit pernapasan, pada model ditambahkan pengendalian berupa tindakan pengobatan (u1) dan reduksi emisi polutan udara melalui upaya pemerintah dalam mengurangi masuknya polutan (u2). Penyelesaian masalah kontrol optimal dilakukan dengan menggunakan Prinsip Minimum Pontryagin dan simulasi menggunakan metode Runge-Kutta orde 4. Berdasarkan analisis yang dilakukan, diperoleh bahwa sistem tidak stabil di sekitar titik kesetimbangan bebas penyakit dan stabil asimtotik di sekitar titik kesetimbangan endemik. Kemudian juga dilakukan analisis keterkontrolan dan keteramatan sistem, dan diperoleh bahwa sistem bersifat terkontrol dan teramati. Dengan menggunakan Prinsip Minimum Pontryagin, diperoleh bahwa kontrol u1 dan u2 yang diberikan sangat efektif dalam menekan polusi udara terhadap penyebaran penyakit pernapasan. Kontrol yang diterapkan dapat menurunkan jumlah individu terinfeksi serta meningkatkan kualitas udara melalui pengurangan konsentrasi polutan.
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The increase in air pollution due to industrialization and urbanization activities has become a serious problem for public health, especially in triggering respiratory diseases. Air pollutants, consisting of certain particles and harmful substances, are known to have a direct impact on respiratory function. In this Final Project, we discuss an air pollution model that influences the spread of respiratory diseases, consisting of three variables: the susceptible population S(t), the infected population I(t), and the concentration of air pollutants F(t), with S(t) being the additional variable introduced after model modification. The spread of respiratory diseases is represented through an SIS model to describe the transmission within the human population. Furthermore, to reduce the number of individuals infected with respiratory diseases, the model incorporates control measures in the form of treatment (u1) and reduction of air pollutant emissions through government efforts to limit pollutant intake (u2). The optimal control problem is solved using Pontryagin’s Minimum Principle and simulated using the Fourth Order Runge-Kutta method. Based on the analysis conducted, it was found that the system is unstable around the disease-free equilibrium point and asymptotically stable around the endemic equilibrium point. An analysis of the controllability and observability of the system was also conducted, revealing that the system is controllable and observable. By applying Pontryagin’s Minimum Principle, it was found that the controls u1 and u2 are highly effective in mitigating the impact of air pollution on respiratory diseases. The implemented controls are able to reduce the number of infected individuals and improve air quality by lowering pollutant concentrations.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Kontrol Optimal, Penyakit Pernapasan, Polusi Udara, Prinsip Minimum Pontryagin, Air Pollution, Optimal Control, Pontryagin Minimum Principle, Respiratory Diseases
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA372.B9 Differential equations--Numerical solutions. Runge-Kutta formulas--Data processing. Q Science > QA Mathematics > QA401 Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Salwa Nuriska
Date Deposited:	30 Jul 2025 06:39
Last Modified:	30 Jul 2025 06:39
URI:	http://repository.its.ac.id/id/eprint/124000

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